Can I render a normal map into a diffuse texture?
First solution (more complex)

The tiled aspect of the normal map needs a specific UV map (I'll call it "tiled"). And your diffuse texture needs its own UV map (I'll call it "UVmap").

Making "tiled" is the first point : if your model is complex or if its "natural" UVmap is very curvy, it will be hard to handle how to tile it correctly without unwanted deformations.

As an exemple : 


The base model (here a plane), and its UVmap :

Add a second UV map (1) and eventually rename it "tiled" (2), then scale it (3) in order to give the tiled aspect





For the example I used this normal map :





Setup your material nodes (here I have put a noise texture but that can be what you want ; there is a lamp in the scene but it is not mandatory)


Add a "UV map" input node and set it to the "tiled" UV map (1)

Connect it to your normal map image texture (2)

Set it as a normal map (3) and connect to the normal input of the shader

Add an image texture for the bake (4) (I presume you have create an image for that) and remember this node needs to be selected when you will bake (the selection defines it as the bake target)




The bake itself :


Make sure your "standard" UVMap is selected for rendering :


Go to the rendering tab and bake section. Click the bake button.


Second solution (simplier)

Make a tiled texture from your normal map texture (using for instance the "small tiles" filter in Gimp).

The principle is the same as above but you'll need only one UVMap as the normal map is already tiled.

Third solution (simplier too)

With one normal map, simply configurate your material like this, using a vector mapping the defining the values (here 10) for the scale :